Question

a wooded piece of land is 68 and 3/4 Acres if 4/5 of this land is cleared for development how many acres of wooded land will remain1. 13 3/4 acres2. 55 acres3. 14 1/8 acres4. 49 acres

Answer 1

To answer this question, we need to take into account that we have here operations with mixed fractions. Then, we can pose the operations as follows:

1. We have a total of 68 and 3/4 acres.

2. How many acres of wooded land will remain if we subtract 4/5 acres from the total?

Then, we can proceed as follows:

`68(3)/(4)=68+(3)/(4)=(68\cdot4+1\cdot3)/(4)=(272+3)/(4)=(275)/(4)`

Thus, we have that 4/5 from the total is:

`(275)/(4)\cdot(4)/(5)=(1100)/(20)=(110)/(2)=55`

We have that 55 acres are cleared for development. We have at the beginning 275/4 acres (68 plus 3/4 acres). Now, we need to subtract 55 acres from the latter. Then, we have:

`(275)/(4)-55=(275\cdot1-55\cdot4)/(4)=(275-220)/(4)=(55)/(4)=(52)/(4)+(3)/(4)=13+(3)/(4)=13(3)/(4)`

Therefore, there will remain 13 and 3/4 of acres of wooded land (first option).

(As we can see this last value is 1/5 of the total acres of the wooded piece of land.)